Local Government New Zealand says it wants dog control laws changed so that any dog on the banned list that is already in New Zealand would be compulsorily neutered.
Five breeds of dog are banned from entering the country. Four of them, the Brazilian Fila, Dogo Argentino, Japanese Tosa, and Perro de Presa Canario, were banned 10 years ago.
A fifth breed - the American Pitbull Terrier - was added to the list in 2011.
However, there are still 3962 registered dogs of those breeds in the country - the large majority of them pitbulls.
Under the Dog Control Act, all animals already in New Zealand before their breed was banned had to be registered with their local council as a "menacing" dog.
That meant they were subject to being de-sexed, but only if their local council called for it - and not all of them do - which allowed for the breeding of those dogs to continue.
That's a loophole that Local Government New Zealand president Lawrence Yule wants to get rid of.
"If we've identified five breeds that can't be imported into New Zealand, it doesn't make any sense that the dogs we have of those breeds continue to be allowed to breed, and that's just what I would regard as a farcical situation where the law actually doesn't line up in different parts."
Mr Yule says he wants a change to be introduced that would make it compulsory for all dogs which fall under those five banned breeds to be neutered and he also wants a review of the law.
He says unfortunately horrific attacks, particularly on children, are still occurring.
Mr Yule says the law needs to be reviewed to ensure it's as effective as possible in minimising the harm both to humans and to other animals.
Local Government Minister Paula Bennett says she is considering setting up a working party involving dog breeders and local government to review dog control laws.
After the vicious mauling of seven-year-old Japanese girl Sakurako Uehara earlier this month, Ms Bennett said she wanted to look at what could be done to protect people from dangerous dogs.
She now says she's open to reviewing the Dog Control Act.
Ms Bennett says the idea of compulsory neutering of some dogs was raised in a recent meeting she had with Mr Yule but it's too soon for her to take a position. She says it's an incredibly complex issue that doesn't have an easy answer.
American Pit Bull Terriers Association spokesperson Karen Batchelor says the idea of compulsory neutering is ridiculous.
She says if it were to go ahead, dog owners and breeders will be forced to go underground, which would make it harder to control them and their dogs.
"You'll stuff your shelters to the gunnels with abandoned dogs, seized dogs, your kill rates will go through the roof and so will your dog bite stats because you're not addressing the problems and the problems are bad ownership and we need to attack it from that angle."
Ms Batchelor says the idea of compulsory neutering is more about discrimination, than improving public safety.